(navigation image)
Home American Libraries | Canadian Libraries | Universal Library | Community Texts | Project Gutenberg | Children's Library | Biodiversity Heritage Library | Additional Collections
Search: Advanced Search
Anonymous User (login or join us)
Upload
See other formats

Full text of "Survey of the QH-50 DASH system."

DUDLT?Y KITOX LIBRABY ^ 
1TAV.^:.L PC5'i;G-P«ADnATE SCHOOL 
MOKTBEBY, CALII^ORDIA 93G43-S0OT 



NAVAL POSTGRADUATE SCHOOL 

Monterey, California 






THESIS 






SURVEY OF THE 






QH-50 DASH SYSTEM 






BY 






Robert S. Paskulovich 






June 1987 




Thesis 


Advisor: H.A. 


Titus 



Approved for public release; distribution is unlimited 



T234318 



UCU«i''>' ClAS^ifiCATiON Of Thi? P:iC£ 



REPORT DOCUMENTATION PAGE 



la REPORT SECURITY CLASSif iCATiON 

UNCLASSIFIED 



lb RESTRICTIVE MARKINGS 



2a SfCL^R'TY ClASSiEiCATiON AuTmORiTy 



.'b OEC.ASS'fiCAT^ON . OOWNGRAOiNG SCHEDULE 



) OlSTRlBUTlOM/ AVAILABILITY OF REPORT 

Approved for public release; distribution 
is unlimited. 



i PEREORMiNG ORGANISATION REPORT NUM8ER(S) 



S MONITORING ORGANISATION REPORT NUV8£fl(S) 



63 NAME Of PERFORMING ORGANIZATION 

Naval Postgraduate School 



60 OFFICE S'MSOL 

(It tpphctble) 

67 



7i NAME OF MONlTORiNG ORGANISATION 

Naval Postgraduate School 



U ADDRESS Gry Sntr inti /IP Codt) 

Monterey, California 93943-5000 



7b ADDRESS (Cfy Sttfe *nd :iP Ccxie) 

Monterey, California 93943-5000 



8a NAME OF FuNDiNGi SPONSORING 
ORGANIZATION 



8b OFFICE SYMBOL 

(If ipplic*bi«) 



9 PROCUREMENT INSTRUMENT IDE N TiFiCA TlON NUM9ER 



ac ADDRESS (Cry S(*te ind ^IP Cod*} 



10 SOURCE OF FUNDING NUMBERS 



PROGRAM 
ELEMENT NO 



PROJECT 
NO 



TASx; 
NO 



WORK UNIT 
ACCESSION NO 



T ',E {include Secu'iry CUuifiatior) 
SURVEY OF THE QH-50 DASH SYSTEM 



PERSONA, AuTmOR(S) 

Paskulovich, Robert S. 



jj -yPf OF REPORT 
Master ' s Thesis 



3d 'ME COVERED 

FROM JAN,85_ "OJUE-BJ. 



U DATE OF REPORT (Yt^e Month OjyJ 

1987 June 



IS PAGE COk^NT 

78 



■6 SuPPlE VENTARr NOTATION 



COSATi CODES 



' E1.O 



GROUP 



SuB GROUP 



'8 SuBjECT terms iContinut on reverit if nt(tiS*ry tnd identify by block number) 

QH-50, DASH, RPV, HYTAL (HYbrid Terminal Approach Landing) 



9 -ABSTRACT (Continue on rtvfrtt if ntitiHiy *rtd idtntity by block numbtrt 

The role of RPV' s as platforms for tactical reconnaissance is steadily growing in 
importance, and their development is receiving attention by aerospace industries the 
world over. This thesis focuses on the superannuated QH-50 DASH system, which has the 
potential for being refurbished and returned to useful operational serviceability. Of 
fundamental import to this end is the need to perfect the launch and recovery control 
systems of this aircraft. A survey is done of the system as it exists today, along 
with an investigation of its control system. 



:0 S"R'9uTiON ' AVAILABILITY OF ABSTRACT 

CS^NClASSiFiEOUNl'MiTED D same as RPT QOTiC USERS 



21 ABSTRACT SECURITY CL-ASSif ICATION 

UNCLASSIFIED 



iU NAME OF RESPONSIBLE NOiViOUAL 
H.A. Titus 



iib TELEPHONE f/nc/ud# ArttCodt) 

(408) 646-2491 



Uc OFFICE Symbol 
62TS 



ODFORM 1473. 8a MAR 



83 APR edition n^tf b« u»ed oitii e«h*utted 
All othfr editiont »it Obsolete 



SECURITY Classification of 'his page 



Approved for public release; iistr ibut-ion is unlimited 

Survey of the 
QIi-uQ DASH System 

by 

Robert S. Paskulovich 
Lieutenant Commander, United States Navy 
B.S., Wayne State University, 1375 



Submitted in partial fulfillment of the 
requirements for the degrees of 



MASTER OF SCIENCE IN AERONAUTICAL ENGINEERING 

and 
AERONAUTICAL ENGINEER 



from the 

NAVAL POSTGRADUATE SCHOOL 
June 1987 









r\r^r 7 i 



■J i. 



!\r 



a. 5 platiGrms frjr tactical 



:1 C V £ L .J p p.: e t i t 



I- , , 



v-BC'i^ 1.V it\£ a '^ oc£.~ 1 on ^y ieruspa 



. 1'^ 



o ^. J. 'w .":> 



laiLi thesis 



jiii -oJ j.AL'i.1 system^ which 



i _n_ '.ica Cij 



li':l^ uLit; 



on the o;-.peranfiua!;ed 



ref -irbi sncd ai'.d returned to easeful cpei-atijnal 

■serviceability. Of fandamentdl import to this end is the 

u recovery control syste.as of 



r:eed to p«rf-_-_-t the launch and 



Dhis u.ircraft. A survey is done of the system as it exist: 
today, alofig" with an investigation of its control system. 



fycSfS 

TABLE OF CONTENTS 

INTRODUCTION 10 

A. 2A'^:^3ro':nd 13 

u . vtti J 40/ OfAOil o J o 1 Ci/J ~J . ■.-% i -J O X t- 

C. oCOrS OF TE:E3I3 14 



DESCxRIFTION OF THE aH-50 



CONTROL SYSTEM IIANDOFF 



1 c 



A. BRIEF OPERATIONAL HISTORY 15 

3. BASIC OPERATING CHARACTERISTICS 15 

III. MODEL BASED 'JPON EQUATIONS OF MOTION 19 

A. GH-50 EQUATIONS OF MOTION 19 

3 . DEVELOPMENT OF THE MODEL 21 

C. RESULTS OF THE MODEL 26 

IV. THE LANDING PROBLEM Co 

A. GENERAL CONSIDERATIONS 35 

B. SHIP MOTION CONSIDERATIONS 37 

C. AUTOMATIC LET-DOWN ' 39 

1. Collective Pitch System 39 

2. Automatic Let-down Scheme 43 

3. Let-down Control Law 50 

V. SURVEY OF HYTAL CONTROL ALGORITHMS 53 

A. BACKGROUND OF HYTAL CONTROL ALGORITHMS 53 

B. RESPONSE OF COUPLED LONGITUDINAL MODEL 54 



63 



VI . CONCLUSIONS 35 



VII. RECOMMENDATIONS 56 

A. GENERAL C^ 

B. SPECIFIC ee 

APPENDIX A: SIMPLIFIED MODEL EASED ON EQUATIONS OF 

MOTION PROGRAM 67 

APPENDIX B: COLLECTIVE ANALYTIC TIME RESPONSE 72 

APPENDIX C: COCPLED LONGITUDINAL MODEL lODE 

RESPONSE PROGRAM 7 4 

LIST OF REFERENCES 75 

BIELIOGRAPKY 76 

INITIAL DISTRIBUTION LIST 77 



LIST OF TABLES 

I. SELECTED DIMENSIONS AND GENERAL DATA 16 

II. COLLECTIVE ANALYTICAL BLOCK DIAGRAM 

44 



LIST OF FIGURES 



o . 


, 4 


■J . 


, 5 


o 


, 6 




-7 


J . 


P 


3. 


9 



4. 


2 


4. 


3 


4. 


/I 


4. 


5 


4. 





5. 





r^fir.ii-icn of Vector Components 22 

Cocr-liiiate Axes , 23 

Orientutioti c-f Airoraft , . , ,,.,.,...,., , . 24 

Coordinate Transformation Matrix 23 

Response to 100 -Pound Force in X-Axis 27 

Response to 100 -Found Force in Y-Axis 23 

Groundspeed in Eai'th-f ixed (Inertial) Axes 29 

Fitch Response to 10 ft -lb Moment 30 

Roll Response to 10 ft-ib Moment 31 

3. 10 Yaw Response to 10 ft -lb Moment 32 

4.1 Qualitative Sketch of the FLow Field at 

Position of Maximum Pitching Moment 33 

HYTAL Control Scheme 40 

Collective Analytical Block Diagram 42 

Collective Pitch Time Response 45 

Collective Pitch Phase -plane Diagram 46 

QH-50 HYTAL Control System 49 

HYTAL Coupled Longitudinal Model 55 

5. 2 HYTAL Distance/Velocity Response 56 

5. 3 HYTAL Collective Response 57 

5.4 HYTAL Collective Response 'Expanded Scale) 58 

5.5 HYTAL Altitude/Vertical Velocity Response 59 



5.6 HYTAL Altitude/Vertical Velocity Response 

( Expanded Scale ) 60 

5 . 7 HYTAL Pitch Response 61 

5.G HYTAL Pitch Responss (Expanded Ccale) 62 



TABLE OF TERMS AND AE3-REVIATI0N: 



A lateral cyclic pitch (rad; 

AFCS Automatic FliB^'it Ccatr^l System 

CG center of mass 

£ acce lerat icn due to gravity 

jW gross weig:.~ 

Ei altitude (above mean sea level) 

H-.. coaimanded altitude 

ilp horsep'jwer 

1.-.^. momerit .^f inertia about roll axis 

1 •. . aiornent ',^f inertia about pitch axis 

cv observer gain (continuous) 

K' observer gains (discrete) 

L moments about X axis 

M moments about Y axis 

N moments about Z axis 

F roll rate in body axis coordinates (rad/sec) 

Q pitch rate in body axis coordinates (rai/sec) 

R yaw rate in body axis coordinates (rad/sec) 

rpm revolutions per minute 

RPV Remotely Piloted Vehicle 

S Lfctp lac's cpet-'ator 

U longitudinal velocity of vehiole CG in body 

axis coordinates (ft/sec) 

V lateral velocity of vehicle CG in body axis 

coordinates (ft/sec) 

Vo collective actuator voltage (volts) 

W vertical velocity of vehicle CG in body axis 

coordinates (ft/sec) 

X Longitudinal position of vehicle 

X body-fixed longitudinal axis 

Xc commanded longitudinal position, feet 

X' earth-fixed longitudinal axis 

Y body-fixed lateral axis 
Y' earth-fixed lateral axis 
Z body-fixed vertical axis 
Z' earth-fixed vertical axis 
d RPV pitch angle ( rad ) 

Ov pitch angle loop feedback voltage (volts) 

dc RPV collective control deflection 

<t> RPV roll angle (rad) 

"A RPV heading angle 

^c commanded heading 



I. INTRODUCTION 

A. BACKGROUND 

The use and evolutionary development of RPV's is 
increasing rapidly, and is likely to increase much further 
yet. The role of RPV's as targets has been well 
established; they are the cheapest and best way of 
producing the realism which is so necessary to train modern 
missile defenses of all kinds CRef 1]. The extension of the 
role for RPV's to the more active area of ECM or 
over-the-hor izon targeting is well within the grasp of 
modern technology and is being developed rapidly. In any 
military operation involving actual combat, the importance 
of timely, accurate intelligence regarding an enemy's 
position or posture cannot be overestimated. In addition, 
the value of this intelligence is greatly enhanced if the 
enemy does not know or suspect it has been collected. RPV's 
call be of inestimable value in this regard if they have the 
capability and reliability to provide real time intelligence 
and reconnaissance services to the field commander. 

There exists today a large array of experimental 
projects, development projects and operational vehicles, 
including an old and tried concept in remotely piloted 
vehicles, the QH-50 DASH system. The disbanding of old 



10 



aircraft conceived in the past is _ a commonplace military 
event, particularly when it is very difficult to exercise a 
capability in any meaningful way. Aircraft in general, and 
the QH-50 in particular, are not isolated examples of 
cost-saving by removing old equipment from the inventory; 
the same happens to other important areas, such as 
electronic countermeasures and deception aids, 

As for the future, some new claims are being made for 
RFV's, but recent operational history shows that in 
significant tactical operations they are still in their 
infancy. However, the alliance of modern existing 
technology with a really Jam proof data link would open up 
wider operational uses for RPV's. In the case of the QH-50, 
if a perfected control system could be implemented, the 
platform could be further modernized by the installation of 
mission-specific gear, such as: 
^ increasing the fuel capacity 

* fitting GPS navigation for precise positional 
information of the RPV 

* active/passive EW equipment 

* decoy and ELINT gear 

* chaff dispensers 

* acoustic-sensor dispenser 

* reconnaissance packs 

* target laser designators 

* war loads 



11 



In all cases, modular payloads would increase 
flexibility. If equipped with high quality sensors capable 
of performing accurate surveillance and reconnaissance 
missions under a variety of environments and battlefield 
conditions, an RPV can perform vital services in areas where 
manned aircraft are either unavailable or would not survive. 
The i^H-50 exists as an available, potentially adaptable 
vehicle without the expense and safety problems of building 
a new full-scale aircraft. However, the QH-50 system would 
require improvements and updates to be returned to 
operational service; this may not be able to be done 
inexpensively. The gas-turbine engine and mechanical 
machinery to drive the QH-50 coaxial rotor system are 
considered to be efficient and reliable, so any 
refurbishment considered would for all intents and purposes 
have to include control system updates, before any specific 
missions could be considered. 

B. QH-50 DASH SYSTEM STATUS 

Like other RPV's, if the QH-50 recovery system could be 
perfected, the number of highly skilled personnel required 
and the concomitant cost of training and keeping service 
craftsmen would be reduced. Recovering an RPV at the end of 
its mission calls for enormous know-how and ability on the 
part of those operating it. If only one in every two 
recoveries was successful, the cost of the system is clearly 



too much; even success rates . of 90% may net be 
cost-effective. Compounding the difficulties of recovery of 
an RFV at sea are the facts that the radio-guidance command 
on which RPV's rely is vulnerable to ECM (traditionally a 
specialty of Soviet forces), the ship's own elactromaenet ic 
environment, ai'id tiie problems attendant to recovering in 
iiigh winds and heavy seas. 

The possibility exists for the U.S. Navy to give the 
obsolescent QH-50 aircraft a new lease on life, if they 
could be upgraded using cost-saving methods, even though 
there is ViO firm basic operating philosophy for this form of 
RPV. 

Bringing the QH-50 back to operational service would 
require refurbishment of systems beyond the QH-50 itself. 
These systems include a control station to direct the RFV 
throughout its mission. Capabilities of the control station 
would include necessary gear to operate the vehicle, 
controls and displays of the sensors carried by the vehicle, 
and displays of the RPV position, utilizing data obtained 
either from the aircraft itself or from a tracking and 
communications unit. Such a tracking and communications 
unit should contain a jam-resistant data link, such as a 
spread-spectrum RF subsystem developed for approach control 
navigation, telemetry information transmission and command 
data link of the Hybrid Terminal Approach arid Landing 
System. 



13 



C. SCOPE OF THESIS 

This thesis surveys the GH-50 2 ASH RrV system, and the 
technical advancements that have made feasible the 
ref urbisliment of the QH-50. Specifically, information 
regarding the system is collated, and known flight behavior 
examined. A simplified math model based on the equations of 
motion is configured to simulate the QH-50, in order to 
provide qualitative insight into the r-esponse of the 
aircraft. Problems inherent with recovering rotary-wing 
aircraft on ships at sea are examined, and the prospects of 
allying state-of-the-art RPV control systems to the QH-50 to 
allow recovery in sea states up to 5 are considered. 



14 



II. DESCRIPTION OF THE QH-50 

A. 2RIEF OPERATIONAL HIGTORY 

The QH-50 was built by the Gyrodyne Company of America 
to form the airborne component of the DASH (Drone 
Ant i -Gubmar ine Helicopter) weapon system. The SH-50 
followed the successful development of a similar manned 
coaxial rotor helicopter built by Gyrodyne, the YRON-1 
Rotorcycle [Ref 2]. The QH-50 DASH RPV was originally 
planned as part of the U.S. Navy's FRAM (Fleet 
Rehabilitation and Modernization ) program, to add 8-10 
years of useful life to about 140 World War II destroyers. 
The QH-50 first became operational on 7 January 1963. Over 
500 QH-50 drones had been delivered to the U.S. Navy by 
December 1966. The QH-50 is turbine powered; this gives it 
the advantage over gasoline-powered drones, because Navy 
ships carry JP fuel, but not avgas. The DASH was to be used 
to deliver torpedo warloads. 

B. BASIC OPERATING CHARACTERISTICS 

The QH-50 math model used in this thesis is the one 
developed in a study conducted by Lear Siegler, Inc. [Ref. 
C], wheti the QH-50 was being considered as a platform for 
over -the-horizon reconnaissance on non-aviation ships. 



15 



The Gyrodyne QH-50 drone helicoptei: has a coaxial rotor 
system with counter rotating blades eliminating the need for 
a tail rotor. It has conventional helicopter controls - 
longitudinal and lateral cyclic pitch to control fore/aft 
and lateral motion respectively. Heave motion is coiitrolled 
by collective pitch control. Yaw moments are generated by 
the aileron -like deflection of rotor blade tip brakes. No 
cierodynamic surfaces are provided. Stability augmentation 
is provided through an all axis stability augmentation 
system. 

Stability and control data were generated by similarity 
with existing helicopters and corroborated by comparison to 
the limited data available. Specifically, force derivatives 
in forward flight were scaled from available S-58 helicopter 
data, as found in Reference 3. Selected parameters are 
given in Table I. 

TABLE I 
SELECTED DIMENSIONS AND GENERAL DATA 



PARAMETER 


QH-50 


S-58 


BLADE RADIUS, FEET 


10 


23 


BLADES PER ROTOR 


2 


4 


CHORD, INCHES 


13 (ROOT) 
6.5(TIP) 


16.4 


SOLIDITY RATIO 


0.0862 


0.0622 


ROTOR SPEED, RPM 


610 


244 


WEIGHT EMPTY, POUNDS 


1172. 5 




Ivy, SLUG-FT^ 


213.8 




Ix^, SLUG-FT^ 


150.0 




WEIGHT, NORMAL 


2303 




I^v, SLUG-FT^ 


470.0 




Ixx, 3LUG-FT- 


330.0 





16 



Important differences between the AH-50 and conventional 
single-rotor helicopters are as follows. The pitching 
moment due to change in speed is large and destabilising due 
to the high lucation of the rotors from the aircraft center 
of gravity. Absence of tail surfaces causes the angle of 
attack stability to be nearly zero, thus contributing to a 
statically unstable aircraft. Yaw rate damping is low due 
to the abscence of a tail rotor. Directional static 
stability is almost zero because there is no vertical tail 
to provide a stabilizing moment; without a tail rotor there 
is no consideration given to tail rotor torque, Ikx. 

As cited in Reference 4, the automatic flight control 
system of the QH -50 is considered to be controllable by the 
Hybrid Terminal Assist Landing (HYTAL) system, a technology 
demonstrator of an auto- landing system, although it is noted 
that a significant improvement would be to include an 
altitude control loop built around an acceleration sensor, 
which would be integrated to provide an altitude rate and 
altitude displacement signal. Better handling and control 
of the QH-50 hopefully would then accrue during the recovery 
and landing phases of a flight. The currently used 
barometric referenced system is susceptible to the 
deleterious effects of the air flow about the coaxial rotor 
system, because the barometric probe extends through the 
rotor shaft, and senses disturbances caused by the whirling 



17 



blades. The transients in pressure differentials stemming 
from rotor speed fluctuations may cause handling problems. 

The currently flying AH-50's, operated by the China 
Lake Naval Weapons Center's target operations group, are 
reported to be susceptible to turn reversal. When the QH-.O0 
is being operated in the launch/recovery helicopter mode, 
the aircraft will translate in the direction the swashplate 
is tilted. The pitch and roll cyclic in this mode are 
zeroed, so a coordinated turn is locked out, and the 
aircraft will skid when commanded to turn. The control 
feedback system for turn coordination is one area that has 
room for improvement. During launch/recovery, the 
helicopter is operating in what is called maneuver mode. In 
this mode, pitch, roll, and altitude are commanded directly 
by the controller. However, when operated in the cruise 
mode, heading and altitude are commanded by the controller. 
When switching from one mode to the other, undesirable 
transients may occur unless the system being handed-off to 
is initialised to the same commanded heading as the system 
being haiided-off from. Additionally, this commanded heading 
may itself not be the same as the direction in which the 
QH-50 is desired to be flown. In a similar manner, the 
existence of large winds during the handoff procedure may 
necessitate the initialization of control parameters other 
than headirig, such as velocity or attitude, prior to handoff 
to preclude unwanted transients. 



18 



III. MODEL BASED UPON EQUATIONS OF MOTION 

A. iH -^0 HaUATIONS OF MOTION 

A math medal was -leve loped for the AH -50 derived from 
the basic equations of uiotion, as delineated in Roskam [Ref. 
5j. This program was used to aid in the understanding of 
the OH-50 fllgijt dynamics; it is an approximate and 
somewhat crude mathematical model intended to provide 
qualitative insight iiito the behavior of the OH-50. 
Reference 3 indicates that an airframe transfer function 
program, AFTF, was used to compute the denominator, 
numerator, and coupling numerator factors based on the 
aircraft stability derivatives, which were scaled from S -5? 
helicopter data, and on the longitudinal and lateral 
equations of motion. 

It is characteristic of such airframe transfer function 
programs that they are modular in construction. First of 
all, the aircraft is divided into elements, with the 
physical characteristics of each element specified in the 
input data. The influence of each element on the aircraft 
is then summed to calculate dynamic characteristics jf the 
assembled flight vehicle. 

When an element (e.g., rotor) produces a force (lift, 
drag, thrust), the air in the vicinity of the aircraft is 



19 



set in motion. The induced velocities (downwash and 
sidewash) affect other elements by changing their local 
■:tir:;-:peed and ang'le of attack. Interference velocities are 
thuo important and must he calculated accurately. Since the 
Uil 50 nas no tail rotor or vertical tail, and is skeletal in 
construction, aerodynamic ccef f icients obtained are 
f-.uiCtioni; of the rotor only. 

The equations of motion used derive from Wewton's law 
applied to six degrees of freedom, as in the case of 
fixed -wing aircraft. The equations contain inertia, gravity 
and aerodynamic forces. The equations are simplified by 
pretending a plane of symmetry. That is, it was assumed 
that fore-and-aft and vertical translations, as well as 
angular pitching motions are not "coupled" with sideways 
translations, nor with rolling and yawing. 

A change in thrust affects side force, and rolling 
velocity affects thrust; these and other cross-effects are 
usually weak and are safely ignored [Ref. 5]. Furthermore, 
the assumption of small perturbations relieves us of 
nonlinearities as well as coupling, which are exhibited for 
large deflections such as rapid rolls, tight turns and large 
amplitude maneuvers. These predictions require wind-tunnel 
or emperical data. 

Once the model was developed, it was coded into a 
Dynamic Simulation Language (DSL) program that approximates 
the QH-50 system. 



20 



B. DEVELOPMENT OF THE MODEL 

In this math model, the X-Y plane is selected to 
coincida with the plane of symmetry of the aircraft, so that 
tl"ie products of inertia Ixv and I -^ .'. equal zex^o. Since the 
<iH 50 does t":ot have a tail rotor, there are v^o 
i-ons iderat ions of rotor torque. The exact value of l^^ 
( mcraent of inertia about the vertical yaw axis) was not 
available; a value of 220 was assumed. 

The definitions of the vector components used in this 
math .T.odel are shown in Figure 3.1. The orientation of the 
aircraft is depicted in Figure 3.2. The body-fixed 
coordinates are obtained in the following manner, as 
indicated in Figure 3.3: translate the earth-fixed 
coordinate system parallel to itself until its origin 
coincides with the center of mass of the aircraft. Then 
three consecutive rotations are performed. First the 
translated coordinate system is rotated about the Z-axis 
over an angle ^, the heading (or yaw) angle. The resulting 
coordinate system is rotated about the Y^-axis over ari angle 
6, the attitude (or pitch) angle. The resulting coordinate 
system is then rotated about the X^-axis over an angle 4>, 
the bank (or roll) angle. The angles ^i/ , 0, and (p are 
frequently referred to as the Euhler angles. These Euhler 
angles are used to perform coordinate transformations as 
shown in Roskam and indicated below in Figure 3.4. 



21 



pA^yFTx 



CG 







^A )^J 




TVERODYN/VMIC AND THRUST FORCES 



ACCELERATION 'OF GRAVITY 




M^,M, 



vz 

AER0DYN7WIC AND THRUST MOMENTS 




qV^^V 



LINEAR AND ROTATIONAL 
(ANGULAR) VELOCITIES 



Figure 3. 1 
Definition of Vector Components 



22 




x< 



XYZ BODY FIXED (ROTATING) 
X'Y'Z' EARTH FIXED (NON-ROTATING, INERTIAL) 



Figure 3.2 
Coordinate Axes 



23 




EARTH 
FIXED 
AXES 



Y 



Figure 3 . 3 
Orientation of Aircraft 



24 



X' 


cos\p 


- s i t i i/' 






cos^ 





sin^ 




1 








X 


Y' - 


3 in\A 


cos^ 









1 










cos 


- -s i r. 


Y 


z- 


d 





1 

X 




-sin^ 





cos^ 




/V 
c 


s i t"j (^ 


C G 3 


W 




— 




— 




— 




— ^ 


^ 










Figur.3 


3. 4 


C'^ord iriatw 


T r an 


sf QiTH 


sit i o 


n Matr 


1 >c 





Di f f ere:i t ial mc;nent, fores and an^le equations are set 
up in body- fixed coordinates, then integrated and suitably 
transformed to yield rotatiorial and linear velocities, as 
well as pitch, roll and yaw angles. The complete simulati'Dn 
code is listed in Appendix A. 

The link between the longitudinal and lateral equations 
of motion and the airframe transfer functions is the program 
AFTF, as previously noted. The specifics of how this 
program works or how it is invoked are not considsi-ed 
here; the transfer functions obtained are listed in Reference 
3. However, the equations of motion thus developed comprise 
a set ^f linear differential equations, which yield a very 
simplified model that is generic in nature. The program is 
initialised to simulate a QH-50 aircraft in a hover 
condition. One of three possible sets of inputs may be 
chosen to run a simulation: 1) All force and moments set to 
2ero, 2) Any of the three cardinal forces set to any 
arbitrary values while holding all moments to sero, or 3/ 
Any of the three moments set to any arbitrary values while 
holding all forces equal to i:ero. The equations are 
decoupled. The chosen combination of inputs are input via a 
parameter statement, in which rotor rpm and acceleration may 



also bs specified. The force and moment inputs act upon the 
vehicle's center of gravity. 

C. RESULTS OF THE MODEL 

Any variety of arbitrary forces and moments may be 
looked at. Figures 3.5 through 3.7 show the behavior of the 
model in response to 12'0 pound forces applied in eaoh of the 
body-fixed axes; Figures 3.3 through 3.10 show the bei'iavior 
of the model in pitch, roll and yaw in response to moments 
applied about each of the body-fixed axes. 

In Figure 3.5, the velocity response along the 
body-fixed X-axis to a 100 pound force applied for 5 seconds 
is shown. The graph indicates that acceleration occurs for 
the 5 seconds during which the force is applied, then 
reaches a steady -state value. 

Figure 3.6 indicates the response to a 100 pound force 
applied along the body-fixed Y-axis for 5 seconds. As 
expected, given the simplifying assumptions used to derive 
the equations of motion, the response is identical to that 
seen in Figure 3.5. 

Figure 3.7 shows the groundspeed response to the forces 
mentioned above; the groundspeed shown pertains to the 
earth-fixed (inertial) coordinated system. 

Figure 3.S shows the pitch response to a 10 slug-ft'' 
positive moment about the pitch axis applied for 5 seconds. 
The pitch angle increases slightly while the moment is being 



26 



a» 



♦VI 



10 


CJ 




• 


_ 


rvi 


LJ 




1^ 


• 


*• 


C3 



*^ui "- 



X 



-f4 



I3X/133JI iYl 



Figure 3.5 Response to 100-Pound Force in X-Axia 



27 






^ 



C3 

-^ rvi 



C3 



X 



-M 



'~lTO71I3jr7A 



Figure 3.6 Response to 100-Pound Force in Y-Axis 



28 



\ 



\ 



\ 



\ 



\ 



\ 



\ 



\ 



\ 



\ 



\ 



\ 



\ 



\ 



\ iS I i 5 jr 



■V 



«0 .r- 

I 
-, INI 

UJ % 



C3 
C3 



t 
X 



-M 



035711311 ~DJ5Ha5 



Figure 3.7 Groundspeed in Earth-fixed (Inertinl) Axes 



29 




Figure 3.8 Pitch Response to 10 ft-lb Moment 



30 




Figure 3.9 Roll Response to 10 ft-lb Moment 



31 



-I* 



t 



C9 
t 



-»SJ 



m 






■HTJtHMi-»)iar$j 



Figure 3.10 Yaw Response to 10 ft-lb Moment 



32 



applied. When the applied moment is renioved, the aircraft 
pitches nose down. This simplified model does not take int:o 
aocoui-.t dampinjg effects, so that after the applied momet^t ii 
removed, the response becomes an -.nd.-imped sincsoid. 

r' ^^'^re - . J sliOwo tne roi i resp0'r;3e to a ^lo- o ^u^ -xt 



r, eS 



.^nirease;; v^hile the aiometit is beine applies, ■'"her; decx^ea^es 
wnen the mjoment is removed. 

Jigure C.12 shows that the heading angle increases 
durii'ig the applicatiori of a 10 slug-ft" positive moment 
aoout zhe yaw axis, as was expected. 

In all these cases, it is only the initial response of 
the model we are interested in; it is very simplified, and 
dot;s not apply to large perturbations, which must be studied 
in a wind-tunticl or from flight studies of the actual 
aircraft. At any rate, development of the this OE-tS model 
based or^ the equations of motion provides insight into how 
the CtK 00 transfer functions were derived in Reference 3, 
which mentioned the importance '^f these equations .jnly in 
passing while omitting their development entirely. This 
again points to the fact that much of the recent work that 
has been done on the QH-50 has been accomplished despite the 
scarcity of aerodynamic data provided by the manufacturer of 
the QH-50, Gyrodyne. As cited in Reference 3, data were 
gleaned fr^m all possible sources and compiled to form a 
basic data bank. Stability and control data were generated 



33 



by similarity to existing hel i centers and the i-Qsults 
corroborated by comparison to the limited data available. 
7or the purposes of this study, those results are taken as a 
basis for subsequent ctiapters; corroborating their validity 
indepeniem: ly is beyond the s^ope of this thesis. 



34 



IV. THE LANDI NG P ROBLEM 

A. GENERAL CONSIDERATIONS 

The '^itirriate criterion of a successful recovery is a 
controlled touchiicv/n on the intended point of landing. The 
Q.K-.jO has a skid landin*? g'ear fitted to its steel -tube 
chassis, landings on ship become difficult because the 
lariding zone is not stationary. 

The total energy of a compound rotor system in descent 
is composed of its potential energy due to its altitude, 
kinetic energy due to the velocity of the mass, and the 
rotational energy in the rotors. This energy can be used to 
substantially retard the horizontal and vertical velocities 
for touchdown. The kinetic energy of translation is used 
for "cyclic" flare, whereas the rotational energy of the 
rotor is used for "collective" flare. 

Cyclic flare is performed by commanding an aft tilt of 
the rotor. This maneuver not only tilts the rotor force 
vector aft, but increases the force by tending to speed up 
the rotor. The speed-up may be permitted, is so desired, or 
the blade pitch can be increased to maintain rotor speed 
constant. Either action will increase the rotor speed 
retardation. The tilted and increased force resolves into 
components retarding the horizontal and vertical velocities. 



35 



Collective flare also may .be used alone or in 
conjunction with cyclic flare to retard the vertical 
descent. By commanding a rapid and collective increase of 
blade pitch to near-stall values, a transient increase in 
rotor lift is produced. This action causes rotor rpm to 
drop off. Thus, flare performance is dependent on rotor 
kinetic energy, i.e., on rotor rpm at the beginning of the 
maneuver and the inertia of the rotors. 

If the collective flare is performed after glide and 
cyclic flare, the vertical rate of descent will have been 
retarded partially, leaving less work to be performed by the 
rotors in collective flare. Collective flare from vertical 
descent is desirable in the case of the QH-50, which will be 
landing aboard a ship at sea in a small landing zone. 

As an aside, during power-off descents, when the 
rotor-craft's drag essentially equals the vehicle weight, 
the system will be at is equilibrium rate of descent. The 
drag coefficient varies with flight speed, rotor solidity, 
and blade coning, and is maximum at low speed. However, it 
is not the present concern to investigate the case of 
autorotative descent and landing; a basic premise is that 
the QH-50 will have full power available during all phases 
of the recovery. 

It is overly optimistic to expect that an operator 
maiiually controlling a QH-50 could smoothly land it on a 
ship at sea in any but the calmest of sea states (i.e., sea 



36 



state 2 or less). Even under these benign conditions the 
tendency of the rotors is to produce its own gusty air, as 
recirculation can occur in its own rotor wake. Adding to 
this are the unseen currents as the ambient wind gets 
distorted by the ship's structure or other obstructions. 
Notiuniform flow patterns may require nonstandard collective 
or cyclic positions that would surprise an unsu.^:pect in^ 
cotitro 1 J. er . 

For example, if, because of recirculation, the dc'wnflow 
is stronger on the left side, the aircraft may tend to move 
backward because of the ninety-degree lag in flapping. Not 
only would the cyclic pitch be effected but the increased 
downflow would look like a climb condition--which requires 
more power to the rotors. This represents a decrease in 
ground effect. Around a ship, these airflow changes will 
generally come on suddenly during a takeoff or landing. 
Additionally, if the aircraft was low enough it would be 
subjected to a pitching moment, because the freeboard of the 
ship acts in effect as a step ground plane; see Figure 4.1. 

B. SHI? MOTION CONSIDERATIONS 

The ship motion parameters that affect recovery are 
pitch, roll, heave, surge, sway, and yaw. Of these, 
available literature indicates that the motions that 
contribute critically to the lariding problem are heave and 
roll. It has been determined that the flight 



FLOW 
STREAMLINES 




POSITIVE MOMENT 



RECIRCULATION REGION 
k V v> ^ 'v ^ — "T-": — \ V ^ V' 



\ \ a: — ^: — "; — <;^ — '^^ — V'^ — «: — ^"^ 



• STEP GROUND PUNE 



Figure 4. 1 
Qualitative Sketch of the Flow Field at 
Position of Maximum Moment 



characteristics of the QH-50 have made feasible the 
possibility of heave motion tracking, leaving the major 
difficulty of dealing with roll in high sea states to be 
solved. 

Reference 3 develops a ship roll predictor that 
indicates a let-down sequence and provides an output signal 
proportional to the time-to-go until the desired touchdown 
time. The time estimates are used to control the descent 



38 



rate via collective control inputs. In this scheme, a 
landing sequence is initiated with the helicopter in a 
hover. It begins its let-down so as to reach the flare 
altitude two seconds prior to the desiied touchdown time. 
The last two se._ands allows the closing rate between the 
helicopter and ship to be reduced exponentially as the 
aircraft flares for a landing. 

Reference 3 also considered the efforts that had 
previously been done to use a cable winch landing assist 
device. The study indicated that ship roll motion 
experienced in rough seas occurs at a magnitude and 
frequency such that the QH-50 could not keep up with the 
corresponding lateral movement. Peak QH-50 roll angles over 
nine degrees would be required in sea state 5. At very low 
altitudes, such peak roll magnitudes, with concomitant 
rates, are deemed intolerable. 

C. AUTOMATIC LET -DOWN 

1. Col lective. Pitch System 

The implementation of the automatic let-down scheme 
delineated in Reference 3 would be subject to improvements 
in horizontal position control. Beyond use of a cable 
device, the only means apparently available that has ti.ie 
necessary accuracy is an optical tracking/ranging device 
developed as one component of the HYbrid Terminal Assist 
Landing ( HYTAL ) system; this device has the ability to give 



positional accuracies of plus or ' minus a few feet. The 
automatic let-down technique gives promise of providing for 
successful recovery of the QH-50 in high sea states. The 
optical tracker/ranger of the HYTAL system, shown 
schematically in Figure 4.2, has the necessary precision to 
position a hovering QH-50 directly above the intended point 
of landing. 



CONTnOL DATA SIGNAL 



RPV RPV 

DATA CONTROL 



IBETBOREF 



L6CT0H 



PAfiGE MO ST f^ ml 



H£AMirjG -Z OEU 



RPV RF 
SUBSYSTEM 




CENTRAL 
VICRCPROCESSOB 



TRACKING SIGNALS 



nPV COOnoiNATES 



CO'^'-'anO 



MASTER 
OISPLAV 
CONTROL 




SEA SURFACE 



Figure 4. 2 
HYTAL Control Scheme 

This technique envisions commencing a final descent 
to touchdown from a standby position hovering approximately 
40 to 50 feet above the landing platform. It was concluded 
that it would be impractical to actually measure the waves 
in front of the ship because of the need for a wave motion 



40 



sensor, and the inability to project for enough into the 
future ''approximately 10 seconds), to permit the QH 50 to 
'wOUiiiience its let-down 'io as to touchdown when roll an^le is 
zero. This approach wa.3 discarded in favor of one that 
n:oc-rled th^ oni^-^'s motion, then operated essentially at an 
accelerated time soa.e, effectively projecting" the ship's 
behavior into the futi.4re, Previous studies of ships' uiotiori 
indica.ted that the two motions of heave and roll were the 
most imt'ortant, and tiiat the others could be ignored. 

The roll motion was then simulated as a second-order 
model. A model of heave motion was not deemed possible, so 
the technique requires the QH-50 to track the vertical 
motion of the ship. This requires that the descent rate be 
very carefully controlled by collective control inputs, so 
that the ^K-50 touches down at a nominal rate of 2.4 feet 
per second. 

Of fundamental import in achieving this heave-motion 
tracking is the response time of the collective pitch 
system. Frouty [Ref. 6] indicates that helicopters react 
remarkably fast to control inputs. Figure 4.3 shows the 
collective analytical block diagram for the Q.H-50. This 
diagram depicts part of the automatic stabilisation and 
control system designed to stabilise the RPV; it also 
accepts maneuver conimands from the remote controller. It 
must be noted that the altitude reference used in this 
diagram is taken to be a radar altimeter; radar altimeters 



41 




Figure 4.3 Collective Analytical Block Diagram 



42 



are not currently installed on the QH-50. Values of the 
parameters of the individual blocks are given in Table II. 
The value of the first limiter is + 40; the value of the 
second limiter is + 12000; the value of the third limiter 
is taken to be to +20. 

The time response of this collective pitch system 
was simulated on the computer; the code is given in 
Appendix B. With the initial altitude arbitrarily set to 
zero, a commanded altitude of fifty feet was input. Figure 
4.4 shows that the blade angle increases to four degrees in 
approximately 0.7 seconds; Figure 4.5 shows the phase-plane 
disigram for the collective pitch change. 

This appears to be a rather rapid response; 
however, it does not directly show how long it takes for the 
QH-50 to actually begin a climb from hover once commanded. 
Reference 3 states that the collective axis dynamic is 
such that there is a lag of 4.7 seconds between collective 
displacement and altitude rate response; this reference 
also suggests a modification to the existing AFCS to 
increase the system gain and thereby appreciably improve 
this characteristic. With this characteristic, the 
assumption remains that heave-tracking is possible. 

2. Automatic Let-down Scheme 

The roll predictor model used is a representation of 
the equation 



43 



TABLE ri 
COLLECTIVE ANALYTICAL BLOCK DIAGRAM PARAMETERS 

Paramet-ST Value 

f X '.' 3 ) 0. 22 



4? ■ r- \ 



(0. 22S ^ 1) (0.0127S + 1) 



(0.22S + 1) 
f-.(S) 0. 3343(0. 177S + 1)(0.0064S + 1) 



[7 3 Y + 0.6S + l| (0.2274S + 1)(0.02274S + 1 

I\i20ny i20n J 



f^'S) 2513. 16 

5.3163 + 1 



f^v'S) 13.53 

C13.5S + 1) (0.01063 + 1) 



K»n 2 . 02 

Kt. 3.875 

Ko.-.- 0.075 

Koc.- 0.05336 

i^^ 24.64 

K.'. 0.015 

Ki.u 0.204 

44 



m 



a 


UJ 




«n 




B 




a. 




in 


^ — 




tn 






^ 


LJ 


H- 


.-UJ 




inj^ 


T 


o 


O 


^ 


>— 




Ql. 


►— 






UJ 




>• 


o 


— • 




1- 




o 




UJ 




_l 




_J 


en 


o 


• 


u 



M 



"S 5 S J 1 £ J"« 

• •••••. 

^ 'V n i\j «- C9 a 



[S93iJ03G) DMi 



Figure 4.4 Collective Pitch Time ResponEe 



45 











a 












U1 










. 


in 












• • 












* 


\ 










a 


\ 










. • 


\ 










»» 












in 












■" E 












O Q 












• 












•^-; lij 
























-"^y iu 












M- in 












THC 
PHFI 












-. ^ 






i 






IN* — 






\ 






»~ 






\ 






u 






\ 






LU 






\ 






_J 






\ 






in d 






\ 






o 






\ 






a 






^^ 






h. • 






\ 






r- 






\ 






« ^ 












in 












_ • 












o 




• 








'o 


«!> 


i i i 


<l 


A^^d 


to 


%n ^ m 


*v< 


»• 






lOQill 





Figure 4.5 Collective Pitch Phase-plane Diagram 



46 



J +- ,j -t- 

the soiutioti to wtiich i.j 

$i-) - A .i;:p j-^uj.,t| sin'uut - v;^) 

VvLere ^ ai^d tUr. are pred6tern:ir.ed constafits and A and ^ 
ari deterTiined from the initial values fcr 4> and d4>/dt. 
This predictor modal is used to initiate a let -down 



tl 



■jat eieht secoiids later the QH-50 touches dowr:. The 



i.e-~G.own IS ■wneoKc:d a^ 



ed 



4 seconds ar^d 



seconds, with an 



automatic abort sequence if prescribed limits are exceeded. 
The descent rate is controlled via the collective axis, and 
includes a flare mode so that the QH-50 is descending at r.o 
;iiOi <5 tl'ian 2.4 feet per second at touchdown. 

This technique assumes perfect horisontal positionine, 
which would be quite difficult for an operator to achieve 
;nar;Un.l-y iri the preset'ice of the unsteady around a ship. The 
ciutoinatic let-down scheme is 
ass-.mpc...Oii3 ■ 



♦'^ direct control of the QH-50 collective pitch system is 
quick enough to etiable the QIi-50 to follow the ship's 
heave motion, obviating tc'.e need for a heave motion 
predictor 

I' hw'Ver site position is maintained automatically in spite 
of .ros-iwitiis and other external forces; that is to 
say, lateral and longitudinal control power and se:.- 
sitivity of the QH-50 are adeq-^ate compared to ship roll 
aco e X e r a u 1 oii s . 



47 



+ the above assumption requires automating control in the 
pitch and roll cyclic axes, thereby making the landing 
fi^lly automatic 

♦^ descent from hover can be made after a prediction as to 
when the roll angle •'.■! the ship will be zero 

'^- ship .r.cti_i. prediction is needed for roll only; ship 
pitciii, o'.jrge, sway, arid yaw are ignored 'available 
literature indicates tliat these motions do not cctj- 
trib:-.t.e s igni f icar.tly tc the helicopter landing problem) 

♦= zv-.e QH-50 would have an altitude control loop 'built 
around ati acceleration sensor and a radar altimeter), 
which could be integrated to provide an altitude rate 
and altitude displacement signal (the currently in- 
stalled barometric referenced system senses disturbances 
other tiian local atmospheric pressure about the coaxial 
system caused by the whirling blades) 

■*^ the influence of ship's airwake effects (e.g., airflow 
disturbances from the ship's superstructure) does not 
unduly affect the altitude control in the let -down 
phase 

The ship motion predictor will be used to predict 

the time when ship roll attitude will be zero and to provide 

a continuous update of the time during descent. Descent is 

initiated when the predicted zero-crossing time is at +3 

seconds. The RFV is assumed to have the ability to track 

ship heave motion. Vertical rate command computations based 

on predictor information permit touchdown equally well at 

any point of the heave cycle; the descent rate is 

automatically controlled via collective control inputs. 

Figure 4.6 shows the control system configured 

for automatic control of the QH-50 during recovery. [Ref. 



AIRBORNE SENSOR DATA 



0- 




POSITION 
COMPUTATION 



radar ~— ^ 



baro' 



[I 



baro 



UPLINK DATA 



Ildg 



cmd 



cmd 



U 



cmd 

AUTOLAND-HORIZ (LOGIC) 
AUTOLAND-VERT (LOGIC) 
H 



cmd 



* 



ship 

5 V,- 
snip 



COLLECTIVE 
AXIS 



T~l 



Uh 



± ± 



RPV DIRECTIONAL 
CONTROL 
DEFLECTION 5 



ROLL CYCLIC 
DISPLACEMENT A 



PITCH CYCLIC 
DISPLACEMENT B 



1 



COLLECTIVE 
CONTROL 
DEFLECTION 



C 



FLARE LOGIC 



PREDICTION 
LET- DOWN 
CONTROL 
LOGIC 



Figure 4.6 QH-50 HYTAL Control Syste 



m 



49 



3. T.et-down ("pnt-rnl Law 

The development of the let-down control law is found 
in Reference 7. In essence, the ship's roll motion 
predictor is used to initiate a let-down sequence while 
providing an output signal proportional to the time-to-go 
until the desired touchdown time. This time estimate is 
used to control the descent rate via collective control 
inputs. There are three different modes in the let-down 
sequence. In the standby mode, the helicopter is hovering 
at a fixed height above the deck (40-50 feet). In the 
let-down mode, the descent rate is continuously adjusted to 
cause the helicopter to arrive at flare altitude two seconds 
prior to the desired touchdown time. In the flare mode, the 
helicopter closing rate with the ship is reduced 
exponentially to arrive at the deck with a rate of descent 
of 2.4 feet per second and elapsed time approximately equal 
to two seconds. 

The control law for the standby mode consists merely 
of a differential altitude rate ( h) commai:id proportional to 
the error between observed altitude (above the deck) and the 
reference altitude (e.g., 50 feet). 



50 



The let-down mode is designed to cause the RPV to 
arrive at nominal flare altitude two seconds prior to the 
desired touchdown time. To do so, the altitude rate command 
is adjusted to equal the ratio of altitude change required 
to the time remaining, i.e., 

Ahonul = H - Hrx / -(t:> - 2) 

where U:t-x = flare altitude, and ta = desired time of 
touchdown. This is the relationship which would have to be 
implemented and used as a sink rate command during the 
let-down mode. [Ref. 3] 

The exponential flare law defines flare altitude to be a 
function of altitude rate: 



h^L = f(Ah) 



The final two seconds (approximately) prior to touchdov/n av^ 
used to smoothly reduce the RPV sink rate from the constant 
value of the let-down mode to a lesser value suitable for 
touchdown impact. Since there is a lag between h comniatid 
and h response, a time history for altitude is ne-eded from 
which the time occupied by the maneuver can be computed as a 
function of initial flare sink rate flare entry. CRef. 3] 



51 



Since sink rate during let -down is a function of 
let-down initiation altitude and flare altitude, a 
var iat-ioi'iHj fldrc (:^-i'i^.vy iir.k rat-e in t'tits let -down mode 
affects the flare time and therefore the touchdown time. 



V. SURVEY OF HYTAL CONTROL ALGORITHMS 

A. BACKGROUND OF HYTAL CONTROL ALGORITLMC 

Tlid MYbrid Termiijal Assist Landirig v HYTAL) system has 
been suggested as a system that wcuLi allow full automating 
oJf an -50 recoveries aboard ships at sea [Ref. 3Z . The 
design jf t:his system is documented in Reference 4, v/hioh 
cites the fact that the tv^/o components of the HYTAL system 
have been successfully tested independently. The optical 
component; which functions as a tracker/'ranger , appears to 
iiave tije precision necessary to fully control j. G.II-30 lurir'ag 
ship recovery up to sea state 5, during which waves of up to 
13 feet [Ref. 3] and winds up to 30 knots [Ref. 10] are 

intered. 

Reference develops control algorithms and discrete 
observers fur closed loop control of the RFV flight path 
using the KYTAL system. Implementation of digital control 
could bcr used to improve the flight control capability of 
the S.n-50. 

If discrete measurements of position are taken using 
the tracker /ranger, the discrete Kalman filter can be used; 
'discrete measurements arise when a system is sampled as part 
of a digital control scheme [Ref. 11]. For modern control 
j.pp 1 i'wu.!: loi^is , the discrete Kalman filter is usually :;sed. 



This technology is straightforward and compatible with 
present control methods. 

3. RESPONSE CF COUPLED LONGITCDIMAL MODEL 

Reference synthesizes pitch, roll and vertical 
control lei'o liased .^pot; state variable aiodels ierived from 
dynamics of the airfi'aaie at never, onboard arialog loops and 
actuators. The oiir frame models are based on stability 
derivatives obtained from Referervce 3. A f'^1 1 -system, 
coupled, longitudinal 3th -order model of the aircraft at 20 
knots is derived, and is shown in Figure 5.1. The time 
response of this system was investigated using the 
Interautive Ordinary Differential Equations ( ICDE) program. 
Starting from a referei'ice point of zero, a climb to 500 feet 
and transit to 5000 feet was commanded. The results are 
shown in Figures 5.2 through 5.8. 

Figure 5.2 shows the time response of longitudinal 
position and velocity. Although the response settles on the 
commanded distance, there is a very large overi:ihoot. Also, 
the settling time is less than 15 seconds; clearly, if the 
QH-C0 could transit 5300 feet in less than 15 seconds, the 
airframe aerodynamics would be exceeded. Looking at the 
speed, U, it can be seen that the peak value of 
approximately 1500 feet per second, attained in 
approximately 2 seconds, would also exceed the performance 
limits of the QH-50. 



I 1 

en • " 



S S 



lO -H 

S S S Q S S • (7> 

2 ' 

O 

f- 

Z2 CM Q _ 

O CO <D 

W ' '^ 

a I 

o 



o _ 



(O 



Q 

U 






I r 1 



.Q 


Q 


Q 


Q 


Q 


Q 


(S 


s 


«•! 


11 




• o 


•32 


• S 


•C9 


.(D 


.6' 


• a 


• rf 



Cvl 



UJQC1(S--Q"SJ QOD 

(- . T -• -^ ^ CJ Q 

O) CM <^ I <^ 



I 

X 






Figure 5.1 HYTAL Coupled Longitudinal Model 



55 



IIYTAL CONTROL OF QII-50 






W 
W 







o 




o 




10 


-'^~">v. 


lO 


/ \^ 


o 


/ 


o 


/ 


o 


/ 


-t 


/ , 






LEGEND 




r~) 


/ 


X (EEET) 




O 


/ 


U (K'lysECJ 




OJ 


/ 








f \ ■ 


O 


'/ ^ 


o_ 


' / * 


o 


' / * 




' / ^ 




-7 




J \ 




' \ 




X ^ — "^ 


o 




o 




1 ~ 


I \ 1 1 



5 10 15 

TIME (SECONDSy 



20 



25 



Figure 5.2 Distance/Velocity Response 



56 



o 



Q 

^, 

^~^ I 

H 

o 

CO 



o 



o 
I 







IIYTAL CONTROL OF QII-50 




LEGEND 
D RAD) 

TiK" R.vnr 



10 



15 



TIME (SECONDS) 



20 



25 



Figure 5.3 HYTAL Collective Response 



57 



IIYTAL CONTROL OF QII-50 



o _ 



o- 



CQ 



I r 



0.0 




~1 



LEGEND 
R (RAD) 



1 — 

1.5 



0.5 1.0 1.5 2.0 

TIME (SECONDS) 



2.5 



3.0 



Figure 5.4 HYTAL Collective Response (Expanded Scale) 



50 



IIYTAL CONTROL OF QII-50 



o 

o 




o 

o 



LECKND 
H (FEFT) 







10 15 

TIME (SECONDS) 



20 



25 



Figure 5.5 HYTAL Altitude/Vertical Velocity Response 



53 



HYTAL CONTROL OF QII-50 



o 
o 



o 

o 



U 

in 

> 



o 
o 

I 



o 

o 



W 



o 
o 

a 



o 
o 

lO ■ 
CO 

.1 



o 

o 

I 







LEGEND 
II (FEET) 



TZ^ESLIT 



1^ 

2 



1^ 
3 



TIME (SECONDS) 



Figure 5.6 IIYTAL Altitude/Vertical Velocity Response 

(Expanded Scale) 



G0 



IIYTAL CONTROL OF QII-50 



o 

o 
id 



CO 

o 

CQ 



< o 
W 



Q o 

^, o 




o 
o 







LEr.END 

_Q.{RA1)/SE_C} 

Til TRAD) 
TIIFH (VOLTSJ' 



10 15 20 

TIME (SECONDS) 



25 



Figure 5.7 IIYTAL Pitch Response 



CI 



IIYTAL CONTROL OF QII-50 



o 

o 



en 
o 






^. o 

W 
CO 




Q o 

< o 



o 
o 







LEGEND 

_QmAn/SECL_ 

Til (RADl 
■ Til FH (VOLTS) 



2 3 4 

TIME (SECONDS) 

EXPANDED SCALE 



Figure 5.8 HYTAL Pitch Response (Expanded Scale) 



Figure 5.3, which is: 5;hown in e-y.-psinded tim-e £C:2le in 
Ji^ure 5.4, ihows the time re-spon^e of i tt":giti;di;".al i^'ci ic 
pitch, 5, and col le^-t i ve. The very large traasier^ts for 
'3j.c;i --i'^se tc 50 ra.diiir4S ot lofigitudii'iax ■.lyolic pit'.':", -.u'-d 
10 radiar.3 of colleotlve pitch--are ..nreal ist io, althoush 
these lai^c v,\lueci appear to 'ii-ial itat i vely coxiicide witl'i ':Vie 
rt-2p^i.:ij;as of the i^ng itudinal distance and velocity chcwn in 
"i£ure 5.2. 

Fife'.ire 5. 5, ^hown with an expianded cirue scale in Figure 
5.0, ^h'^'ws similar, ni'ireal ist ic trarisierits for altitude, H, 
and vertical velocity, W. Both steady-state values .rippear 
to b'n' as expected, but the inordinately fast settling times 
c- 1 ►i ar 1 y ar w n o t p c s s i b 1 .^ . 

Filially, Figure 5.6, shown with an expanded time scale 
in Figure 5.7, ;diOws large transient responses in pitch, Q; 
pitch angle, and pitch attitude loop feedback voltage. 

It must be noted that although the final steady state 
responses of this coupled system are v/hat was expec-ted, the 
u;ompressed time scale and large transients are apparently 
u:jrecil ist ic; such behavior in an actual QH-50 wouli be 
beyond aerodynamic and performan^-e limits. 

^ ^.'^\''T^-^r\r rvCTiTTX/ rJAMT'OTTTr 

Eefei'cnce 3 reiterates the fact that there i.s a 
tr^ansiticii point in the control of tb^e 00-50 betweer; the 



63 



cruise and maneuver modes. It is suggested that this 
handoff be made to coincide with the shift between the RF 
and electro-optical ■-omponents of the rIYTAL system. To 
preclude undesirable transitions of the '^H-ZO while £;hifting 
fruin Ui^d-r to mode, it would be necessary to intitialice t.he 
system basing handed -of f to to the values of heading, 
altitude and airspeed of ti^e system being harided-off fr-,aii. 



64 






V:. CONCLUSIONS 

'Zy of tl^iji --nc>9pti.ul ^;ii.n; i;;ac ioi:. r. f z[\^ -ill -; J^ 

Mr-j.:^.- .r aC l". . c^vii.a o.:j,.':: leccV'Try --.If *"l.i^ -xil o0 RFV ;.i". 
■-•-•Lit"! ^^ ^ 3yc It-.;.. 

"^' - ,.„ - , . -_,-.:_. ^ _ j:- .. , , ; J • „ w ,,,, i. _,,.(-; .. i _ ^ .1 _ . ... 

i 1..1 w' .».".—! J w _ _'i.i o J. o ;v '_).;. j-- I '-■ s/ . i-i L 1. j^ civj ;^ Ui.i-J. _ .;. '_ i. " l " '.j. ..'w I , 

.Oi^tr-l '.' i ;j. Co 1 • ect. i Vc: pitch channel, .it i 1 Ic it.j^ 

a p^c" i^^ct- icri jI ohip roll riijticn to permit tc'»ci. i:.£' 

iwY-/n ■_:. a neai ..y ^ev-l .leck. 

The potentially trouble3on;e effect cf ship heave 
iuoticii is clin.ln.^ted by causing the RFV r;o track 
ttic vertical motion cf the landing platform d^^ri-.g 
the let -down. 3y automating the vertic-al axis, 
:i!:'^L:ioe '.jontrcl af touchdov'/n sink rate and toucr.dcwn 
tiiT.c '. wit..'j x'espect to snip rox- raotion) can oe 
aci. 1 eved . 

It appeal's feasible to felly autoujate the ii.ji iwCnt .:j1 
i:.os ItiuCi Coiiti'ul by coupling the information iirovidcd 
by the HYTAL tracker/ranger on the ship to the Oil 50 
cycli: .-axec fligtit control system wiiile utjdei'vay oi:i 
ship's neading. Any serious effort to update the 
Qh o0 TAoH system into a platfoi-m for operational 
sei.vi..,c -»'ould require perfecting this control system 
a w a mi n i mum . 

A suggested equipment package for total modernization 
W'^^ld include a vertical acceleration sensor, radai- 
-il i ..";ie ter , oi' three-axis rage gyros, .and aii iCiterface 
■....Ait to make it all compatible with the HYTAL system. 

oensor packages , e . g . , i •• .-.amera, ii.^k'i, cc.im aeci' 'y;:.as.l 
be dependent up'jn the type of raission taslting 
employed. 

For the QH-5i3 system as it curi-ently exists, possible 
missio::s itiolude beiiig used as an expendable decoy fc: 
-anti --ship missile defense task.s. 



VII. RE COMM ENDATIONS 

A. GENERAL 

A^ the march of science and technology [e.g. , A3RCC and 
LAMF3 A.3W iiel icoi; ters '/ over-rar. the QII-50 and r.ast it along 
the wayside, so may further progress in RPV control systenis 
provide the means for a new lease on life for the C<ri-'10. 
With the successful testing of the independent: elenients of 
the KYTAL system, the time may be at hand to bring the QH-50 
back into operational serviceability. The next step would 
be to configure a refurbished QH-50 for flight testing of 
the full system. 

B. SPECIFIC 

The following specific recommendations are included fcr 
cons ideration ; 

1. The HYTAL control algorithms developed in Reference 
should be implemented. 

2. A refurbished SH-50 should be fitted with a radar 
altimeter, vertical acceleration sensor, and other 
equipment needed under the KYTAL concept. 

3. A land-based trial of the system should be 
investigated. 

4. Determine the QH-50's remaining useful life and the 
operational and financial resources required to endow 
these RPV's with an operational viability and 
survivability commensurate with the challenges and 
demands of identified mission tasking. 

5. Determine the actual cost of refurbishing the QH-.jO. 

6. Determine whether the operational utility of such a 
conversion Justifies the cost of the conversion. 



66 



^i::x 






^ln ici. ..,;a » 



i -. 1 i^ L- 



-^ li _ ^ . J. ^ ._■ i 









t '' 



r r. f t f f + < f * f t. r f. • f f f T ♦ • f ^ '' '■ + r • + • T * t: f +c +: +■ + i- + I * ♦■ ' * *■ f f i * •■ t ' 



r MGMEN' 



>:er?:a 






I'^.^M vJ ^ i- .an i. iL -J 



T A '" ■' A V T '^ 



. fA X A, .• .•'. X : , .-^ if-i i o 

T ' ^ \f ^ -" V A '" 
— ill i , i'lr'^ i , .i^-W 

T-,*.-^ .-n-*f-n ■p'")'^ 

7-, -T-r^.-. r-l r •; ^ -.-, T-, -. ^•, -T^T--,,-. !"■ -^ |^ 1-, T^ ■[-. ,-; 

■p -^ r^ T^ rt T* ' -^ T^ ,'-^ 

■pitch' . (RCIL^ , (YAW 

■- -- , / V , V y /v , J i ru 1 ,-; , ;!, J. 1' ^ ,^ i. / .^ ::'- -V 



* + 



, >: * , t f f- ♦ t + f f + f f t f f *■ » + I f ♦■ T f + + i- f f t + f- f f T f f -f t: -+^ ■+ f- >■ f 1- t * ♦- * ^ +• T t » ♦ t f *■ 
f 



^^r conversion: 



IZMIX = IZZ - IXX 
IXMZY - IXX - lYY 



^ + -r- INITIAL CONDITIONO 
f- 

?0 =0. 

QO ^0. 

RO - 0. 

UC - 0. 

■: •.-. -- --51 



— .^ . 



i. Ia ^ ^ - t^' . 



?£IC = 0. 




WRO ^ WRPM0i<2.PI, 


/■'60. 


ALTO = 0. 




* 




DYNAMIC 




K 




r^+. INPUT CALCULATION' 3 




f- 




j.'..-T - CTRT -*- r'JR 




IF ■ F:.'.. EO. i: THEN 




?x ^ K^'STE?:; 


^ 'TTT-N l-P 



"-T _ -, ^ , -, rrr-,-^. ■ ■- Ttf- r-n ^^ ^"^TT'D/rrvT'^TvN 
— »> . 

M - 2. 

N - 0. 
ELOZIE :FM.EQ.2) THEN 

-J - A> 1 o - i:.r ( r^ 1 rC 1 ; ' o i nr \ cNDT ) ) 

M ^ Y f V GTE? ( STRT ) -STEP ( SNDT ) ) 

N ^ Z + ( STEP.; STRT) -3TEP(ENDT) ) 

EX ^ 0. 

FY = 0. 

F Z - . 
ELSE IF .:FM.EQ.0; THEN 

FX = 0. 

FY :: 0. 



L = 0. 

M = 0. 
N = ,"^ 



f-*^ COCRDINATE TRANSLATION COMPONENTS 

♦'.+ + ^t BODY -FIXED TO EARTH -FIXED ( EHLER ANGLES) 



TRANSvZ;. - C0S(P3I)*SIN(TKT)*3IN(PHI) - SIN(P3I) *CCS': PHI ) 

TRANSvC; ^ C0S(FSI)+SIN(TKT)+C0S:FHI) ^ 3IN:FSI) ♦SIN'FHI) 

tfa:;o,4) = sincPsiv^cos^tht) 

tfans(5) = sin(psi) *sinctht)*sin(fhi) + ccs( psi) *ccs(phi) 

TaANS(6) - SIN(PSr;+SIN(THT) ^C0S:FnI) - SIN;' PHI ^ 003 ( PS I ) 



f 



TFANS(7) - -SIN(THT) 

TRANS ( 3 ) = COS ( THT ) ^3 IN : PH I ; 

TRANS ( 9 ) - COS ( THT ) *COS •: PH I ) 

^■^■^ FORCE COMPONENTS .'SIMPLE MODEL) 
-t. 

FAX - FX/2. 
+ -^>^ FTX SET FOR DASH HOVER 
FTX = FX/2. - GXtMASS 



C8 



f 'K + 



TTTV -T"^ h''^':^' '^' ■"' ' 



'V 



FY/C. 












M-jME''T C'CMPGMEM' 



+ 



.-' X — .1/1-.. 

' ■• -n _ ' .\ T T" 

V -f /* ^" _- V f A \ ."^ 



■'■■' -"'-A't^rri'^AV'.-',!-.- 



f V f. 



IYMIZt-R*Q 

IZMIX^F+R + MAT;. /lYY 

IXMIY*?^Q - MAT; /IZ": 

EQUATIONS 



WD 












r- AMGLE EQUATIONS 

r-:: ^ ? . :Q^£iNTr: 

T:-i70 - Q* cos (PHI ; - 



i; 1 Rt'COOCFHI ' ♦TAM ; Tir 
Rt.SIN^PHi: 



03 



*** VELOCITIES 

K^c*** DASH TOTAL VELOCITY (BODY-FIXED) 
VTOT = SQRT{0'U^>2 + VVf. + 2 f WW** 2^, 

T. 

,^.k.*K* EARTH -FIXED VELOCITIES 

+• 

vert:: - VL'^TRAKS;4) - VV^TRAJ:C'5) + WW*^TEAr;3(C) 

/v^iT-^n - ^- o *^ i ii-ar^ o » I , •» / V * J. ixAi-N o «, j ,i ;• AA^ in-f-.N.w'; .J .' 
V.1 itv.' w iM 1/ •.. r iL il i. 



■^^^IN'TEGRATIONS 

i^-^^ MOMENT EGwATIONS 

? = INTGRL(PO,FD) 
G ^ IN'TGRL(QO,QD) 
E = INTGRL(RO,RD) 

<^*-^ FORCE EQUATIONS (VELOCITIES) 

'ju ^ imtgrl(uo,i;d) 

VV = INTGRL(VC, VD) 
WW r INTGRL(WO, WD) 
* 

■^*'^ ANGLES 

FHI = INTGRL(FHIO,FHID) 
THT - INTGRL(THTO,THTD) 
FSI = INTGRL(FSIO,FSID) 
PHIDEG = RADEG+FHI 
TKTDEG = RADEGi^THT 
PSIDEG = RADEG*FSI 
f 

■*^f-* ROTOR 

WR - INTGRL(WRO,WRD) 
WRPM= WR*60. /(2. *PI) 
'¥. 

**-i^ ALTITUDE 

ALT = INTGRL(ALTO,UVERT) 

CONTRL FIN'TM = 10, DELT = 0.01 

PRINT .1, PIIIDEG, THTDEG, PSIDEG, UU,VV, WW, WRPM 

SAVE 0. 01, PHIDEG, THTDEG, PSIDEG, UVERT, GRNSPD. WRP, UU, VV, WW, WRD 

PARAM FM=0. ,X-0. , Y-0. ,Z-0. ,WRPM0=ei0. ,WRD=0. ,STRT=0. , DUR^.^ . 



70 






IXl^rti n X -J i , -'ill — 1 1-1 K 'J X -J y L ^ ^ Uj ', LI i. - u c- , . .N - O .l'.. . L -1 J. -- jI'^1 V . i ^ - . <_■ 

; o , ^ V — — ' 

U iT.— .J. ^. , J i- , 1^ 4- - i. .jf». _ i w^ ■' .. L. ^j ..■.--_.■,...- ^ ;^ . , . .". . _ i-j J , . . ^ - ^ e. , ... 

V ^' -• I^ L 3 3Z E ^ , L-^^- - C , .. '-Zc , ^ .. -■"■ ; 

'-.t P.-t^^ i. > -J -• , i^il. - i il:i.O J. w ; J. -. .'li- . . ! X .L o , ..,■.■! -'J C >_ . ^j - .J i\^-.. .■■ L -- i. i. , ... 
••V,- . i^. T7 •-■ — rr r7 ^— ■' ~_ r^,~>' " ^ '^7. " t ._ -. \ 
J .^i — -, XL '-J il.i'-lli -^ , i^^.^' — " ■> i-.' .. .-' ■-. - .^ '.. ; ij X - -^ ; 

-J .'-i.-^ ...1. -. -1, ^1-j— i ^- ■. _; .V - ,' i _ .'i^ . 1-1 _ - .4. o , -^ ^H — .^ J. -^ (■ I J ( M i( « - -J , . . . 
_■ .'^ - :' n, ^ . ^. 1:^ ^ , ^ _' — ' n c/' , ^ -^ - ^ V..' ,, —I X ■- -t / 

- - \ T •:• -• -■ r- T- _.,-, r- r >•-.<-. ■, .T, - V ,»^ • » •■ - _ . 7( ' ^ V T _ ~ •" ,-< ■ - "-^ — \ ' V •- _ Q r - \ T _—.■:-, \_» 

-i .v.;.* Lj , -.3 . , I. L, — . ^;V -' .. -./ ' . ^ .'^ij . L ' . — X iw' , <- -■■« — --'j_j -■ ; 11 • -1 i'. 1.1 j. - _ j ■- .1 - . -^ > . ■ 
I^^; 4 ■_• .'. A ■.-' '.- ii x_, iL r^A i' I -■ ^'J ' / 

-■* ^Vt^x i.- . O • J , 4* IL — 1 x,Iv_' ^ ^ ' _ ^ *.'*iL '. . » .- — X C' , w* I -»-^xl* -- / '^ V lL n. i '. i.( ^ — X C , ... 

" ,'^. — • 7 "• -^ _ rr "^ T _ 1 \ 

'^ J^. 'li .,;,,- i — k iJ. f . _ X _' .. X - .il , i4 * — >. c/ , w iN — .^£j\^ .' ,jrUi.N ._'! 4J V -N X ■ X c- , . . . 

r ~ _ _ - -' '^ ~ - ..n '^ '■:M ' 1717 7'" / 7 7? r" ' '-•'-•_ c i- T — -^ >• 

*., ^'— *.^>i.X— jC^.Oj-IwN— xX--1-jx/l.JCj\^ jOw— Oji™)X — ^ ,' 

Z' ^■' ~ 

' Av "7- ' A'P"'^ ■ A"' '^ ' 

x^r^xjw-- , rt^L / ;''^rLv_^ J.N A - xi.''J h'-'UnJc 

r^^RAM FM=l,X-c!. , V^l^C. , Z^0. , WEFM0-610. , WRD=:3. , CTRT=0. . ZUR=5 

-xLi- i_i riC' C xj 

i ' ,.' ■^ 'ATT, T-. 

x^i. .>i^ii.k^ . £ij_ixj / r 

lAEEi •:all; ecrce i:: Z - ISO foumds • 

£NE 

"■ *i \' ■' 7' * ■■■•::■ '~T /ATT -. 
^l\l^ ^IIl^ ^flxjxLxj ', JrM^^ ) 



EARAM FM^2. X-^100. , Y^0. , Z -0. , WRFM0 = ei0. , WRD=:0. , oTI 

-.A.^r^^l! I XjAjJi-iIL ^' ALij ) 



I. ^ — c-' . 1 ..V X J. '• — • J 



APPENDIX 3 
COLLECTIVE ANALYTIC TIME RESPONSE 
f- +, .♦c r r - V t. f ^ t t f It t t t * * * ^ *f *^ * i^ +; * *« * +c -t ♦ i * -f; + + «f * + -^^ ^< f i t: +; f f. i f f * t * * * K t- 

TI^:E RESPONSE :■? '::iE an -so, based on the collective 

*■ analytic BLOCK DIAGRAM * 

f- ROBERT S. PASKLLOVICH ^■ 

^ APRIL 1937 + 

f ¥ 

t *- r f * t: f. ir t * ♦ f >; + If it i. f f +• f I'. * +: f t + t * 1- * + f > * + t * S< * y * +: + * + * * + >■ + + .f t ♦ 

>■ THIS PROGRAM DETERMINES THE TIME RESPONSE OP THE * 

COLLECTIVE PITCH SYSTEM ON THE OH -50 HELICOPTER, ^■ 

^ AND PLOTS THE ASSOCIATED GRAPH * 

ff^^♦^^, tf + * *■■+<(+:*: t:ir f: ))c+- tf +:^*4r**++* + ******4«**** ********* ****** 

TITLE COLLECTIVE ANALYTIC 

PARAM HC-500.0, KH=2.02, KTHC=0.075, Kl=24. 64, K2=0.015, ... 

KLC=0.204, KTHDC=0. 05336, KHDCT=3.375 
ARRAY A : C ) , B ( 5 ) , C : 2 ) , D ( 3 ) , E : 2 ) , P ( 3 ) 
TABLE AC 1)^0.0011328, A(2)=0.1334, A(3)=1.0 
TABLE 3(li-3.G33469E-08, B( 2 ) =9 . 9900E-06 . BC 3 ) =5 . 576E-03, ... 

B( 4) -0.2517315, Bf5)=1.0 
TABLE C .' 1 ) - 1 3 . 5 , C ( 2 ) =0 . 
TABLE DC 1; -13. 5, CC2)=0.0 
TABLE SC1)=0.22, DC2)=:0.0 

TABLE PC l/=0. 002794, PC2)-0.2327, FC3)=1.0 
INCON H--50.0 
DERIVATIVE 

THC - KLC * TH 

TH -^ LIMITC0.0.20. .THCC) 

THCC = INTGRLC0.0, THCDOT) 

TKCDOT - K2 * FF 

PF = LIMITC -12000.0, 12000. CEE) 

EEE = REALPLC0.C, 5. 316.DD^/ 

EE = 2513. 16 * EEE 

DDD ^ TRNFRC2, 4,0.0. A,B,CC) 

DD ^ 0. 3343 * DDD 

CC = REALPLCO.0,0.022,BB) 

3B ^ LIMITC-40.0, 40.0, AA) 

AA = Kl * TACH 

TACH = HHCC - TACH A 

TACHA - ICTHDOT ^ FTH 

KTHDOT = KTHDC ^ THCDOT 



72 



HnC = r'^IiE - HHII 






-( Ar\. r. , ^ij - , ;i..'.- 



:CN': 



■_-.i J. ^j.Cj r.i:,or-^.^. 



APPENDIX C 



COUPLED LONGITUDIMAL MODEL lODE RESPONSE PROGRAM 



SPEC IF I CAT IONS 

VARIABLES i, INITIAL CONDITIONS 
'J - .5. CCi2O0OO300£+C0 

H ^ 0.0000000000E+00 

W = 0. 0000000000Ef00 
- 0. 0000000000E+00 
TH - 0.0000000000E+00 
THFB = 0.0000000000E+00 

B = 0.0000000000Er00 

THC = 0.0000000000E+00 
TIME - 0. 0000000000E+00 

CONSTANTS: 

XC - 5.0000.000000 

HC = 500.000000000 

SPECIAL FUNCTIONS: 

VF ■- -0. 104*(X-XC)-0. 205*U 

VC ^ -0. 191*(H-HC) f0.0864*W-5. 877Gi^TH 

DERIVATIVES: 
D(X /D(TIME) = = 

D(U /D(TIME) = = 

-0. 052 ^U + 2. 22*Q-o2. 2 *^TH + 57. 5*B + 8. 59-^THC 
DCi /D(TIME) = ^ 

-I.0>'W-f34.0*TH 
D(W /D(TIME) = = 

-0. 34+^U-0. 563*W+34.0*Qh-25.0*B 409.0^THC 
D(a /D(TIME) = = 

0. 0313*U-0. 00455*Q-1. 59*TK -40. O^B^l. 48*THC 
D(TH /D(TIME) = = 

Q 
D(THFB /D(TIME) - = 

34. 5*Q+181.0*TH-12. 5 + THFB 
D(3 /D(TIME) = = 

4.91*THFB-46. 3*B+10. 5*VP 
D(THC /DfTIME ) - - 

-47.0*THC+4. G4+VC 

END CALCULATION WHEN TIME .GE. 25.0000 



74 



LIST OF REFERENCES 



F..,l. 1 ioL'iri Liu-itei, 1379. 



■. i- 



I! :i .; 



■auci^ f'-'i.- ^-i u- Av i ,jit I '.u Z\'.if-., rir, :il 



ll/hr.d T^cmL::Ji: As i i s t L^mdi ug ■ UYT AD , NWC TF 533C, 
Fo^rt 1, N:.val Weapons Cat^t-r,, China Lake, CA, 197o. 

Rookarn, J. : Ai rj^ I ^i:ii Flight Cyn^^Tiiia aui Au. i':'^:la.t l 'j 
"light C'^-ut:olSf The otiiveroity of Kausai, 1979. 

FiO-*"iy, ?.W. : Helicopter Aerody u3.mi os / PJC Publ 'L: j.t i :::;n3, 

~ , • -, 1 ■ '. o r 

D'isigu .lad Ana.l/iis of HYTAL Control Al gor i thm--i , Zystems 
Analyois anJ Control, Ridgecrest, CA, 1931. 

H/bnl T^x'mLu^Ll Aasiit L.:uidir.g 'HV^AL:, NWC TF 5933, 
Fart 2, Maval Weapons Center, China Lake, CA, 1973. 

H^ndriokson, R. : The OcircLU .-^/ma^ac.-/ Doubleday, 1334. 

Frost, R. . The jRt- JaiiOn Sec wet :; Seaufoz't For-so yJiiid 
Zpe^^d .iud l^a.ve Height, Scientific Paper NO. 35, lier 
Majesty's Stationery Office, London, 1966. 

L-3wis, F.L.; Optimal E-^ t ir:iai i on, Wiley, 19SG. 



BIBLIOGRAPHY 



iai^H, S.L. Meyers, W.G., and Rc^sigr.ui, O.A. /?■,> -j^^o n5e 

O'f Hel ic^^ptc^v Platform for the US3 Eelk:.jif 
'JZZ QjLrciJ. 'OE-IC'WJ 1 ai ^ Destroyer-;, MSEDC 

Report 3368j N'aval o:\ii: Reseai'ch Developmetic Center, July 



I aU'i, 



Skeyir'ii, 0. : An E:-.pi^r inieitt al I uv-'S t i gat iort of Rotor 

and F I ^<fj Fields in o/'je 7 1 j i nit/ of a Step Ground 

Virgii-;ia 'Jni vex-si ty. Aerospace Engineering Report TR-24, 

J. J u vj . 

Wolkuvitch, o'. and Hoffman, J. A. : stability and Control of 

He I icopters in 3teep Approaches, Volume 1, USAAMRDL. MRI 

Report NO. 2234-1, united States Army Material Research and 
Development Laboratory, May 1371. 



76 









22304-6145 



I ;jrury 



•ar ^-'-« 



■-■j' ) 



' ■ J '^ ^r „• -.^w *^ t 



.i_r.. 



i -r. 4 - ^ * 






1 8 76 7 



vi 



DTTDLHIY r 


'" ' BY 


HAV.AL !- 


i'E SCHOOL 


Mm^v-' 


•lA 93943-8002 



Thesis 

P2535 Pagkulovich 
c. I Survey of tj 

DASH sNiiHrem.